Let's reply to your fencepost-moving question with two questions. At what percentage of the vote does voting for a third party gain utility?
It's a continuous nonlinear function, not a boundary. The utility of you voting for a candidate with anticipated zero chance of winning is zero utility. Vote utility increases as your candidate's anticipated showing increases. Utility is at maximum when two candidates are evenly matched. Utility decreases back to zero as a candidate becomes more certain of winning. This might sound confusing, so I will explain further with some examples.
Daffy Duck is physically incapable of winning. It is absolutely impossible that your vote for Daffy Duck will help determine whether Daffy Duck gets to be President, so a vote for Daffy has a utility of zero.
Vermin Supreme's likelihood of winning in a close race is basically epsilon (http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon). A vote for (or against) Vermin Supreme is more likely to effect the outcome than a vote for Daffy Duck and therefore has a utility of epsilon, which is greater than zero.
Jill Stein's likelihood of winning in a close race is better than Vermin Supreme's, but it's still vanishingly small. A vote for (or against) Jill Stein is more likely to effect the outcome than a vote for Vermin Supreme and therefore has utility > epsilon.
Donald Trump and Hillary Clinton are not just the two most likely candidates to win, but to win in a close race against each other (which is the point). A vote for Clinton or Trump is more likely to effect the outcome of the election than a vote for any other candidate.
Hillary is currently beating Trump by about 8%. That's a really healthy lead. In a universe where she was beating Trump by 0.1% your vote would be even more likely to effect the outcome of the election than it currently does, and its utility would be even higher than it currently is. Likewise, in a universe where Hillary was beating Trump 87% to 4%, a vote for Hillary (or Trump) would have the same utility as a vote for Stein in this universe. You should still vote for Hillary (or Trump) because that's still the action with the greatest relative utility - there's no closer race that your vote is likely to determine - even though its absolute utility isn't as high as your vote in this universe.
Let's say that Obama was allowed to run for a third term. He's more popular than either Trump or Clinton, and he's polling 60%/19%/18%. Your vote is most likely to be a deciding vote between either Obama and Trump or Obama and Clinton but Clinton and Trump are close enough that we can't say who. Stein is so far behind that your vote won't decide the race between Obama and Stein or Trump and Stein. Therefore its utility is maximized (in that universe) by voting for Trump, Clinton, or Obama.
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syntheid
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Date: 2016-08-13 09:12 am (UTC)It's a continuous nonlinear function, not a boundary. The utility of you voting for a candidate with anticipated zero chance of winning is zero utility. Vote utility increases as your candidate's anticipated showing increases. Utility is at maximum when two candidates are evenly matched. Utility decreases back to zero as a candidate becomes more certain of winning. This might sound confusing, so I will explain further with some examples.
Daffy Duck is physically incapable of winning. It is absolutely impossible that your vote for Daffy Duck will help determine whether Daffy Duck gets to be President, so a vote for Daffy has a utility of zero.
Vermin Supreme's likelihood of winning in a close race is basically epsilon (http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon). A vote for (or against) Vermin Supreme is more likely to effect the outcome than a vote for Daffy Duck and therefore has a utility of epsilon, which is greater than zero.
Jill Stein's likelihood of winning in a close race is better than Vermin Supreme's, but it's still vanishingly small. A vote for (or against) Jill Stein is more likely to effect the outcome than a vote for Vermin Supreme and therefore has utility > epsilon.
Donald Trump and Hillary Clinton are not just the two most likely candidates to win, but to win in a close race against each other (which is the point). A vote for Clinton or Trump is more likely to effect the outcome of the election than a vote for any other candidate.
Hillary is currently beating Trump by about 8%. That's a really healthy lead. In a universe where she was beating Trump by 0.1% your vote would be even more likely to effect the outcome of the election than it currently does, and its utility would be even higher than it currently is. Likewise, in a universe where Hillary was beating Trump 87% to 4%, a vote for Hillary (or Trump) would have the same utility as a vote for Stein in this universe. You should still vote for Hillary (or Trump) because that's still the action with the greatest relative utility - there's no closer race that your vote is likely to determine - even though its absolute utility isn't as high as your vote in this universe.
Let's say that Obama was allowed to run for a third term. He's more popular than either Trump or Clinton, and he's polling 60%/19%/18%. Your vote is most likely to be a deciding vote between either Obama and Trump or Obama and Clinton but Clinton and Trump are close enough that we can't say who. Stein is so far behind that your vote won't decide the race between Obama and Stein or Trump and Stein. Therefore its utility is maximized (in that universe) by voting for Trump, Clinton, or Obama.